Workout routine advice?

So I've only just started to go to the gym and I find that I often feel awkward when working out and feel like I'm not getting the best possible workout. What I usually do is spend 20-30 minutes on the elliptical machine and then move on to 20-30 minutes on a bike or treadmill.

My questions are:

• What are your routines when you go to the gym?
• Should I lift weights? (I'm more interested in burning fat then gaining muscle or toning up)
• How accurate are the calorie counters on the elliptical/bikes/treadmills?
• Do weight loss courses on the machines actually work differently then any of the other available options?